Why is my glass plane displaying diffuse at specific angles?
The problem is due to a flipped normal - this can occur when extruding a plane, depending on which way the extrusion is applied.

In the following example one plane is extruded 'upwards' (the left-hand one) and the other is extruded 'downwards' (the right-hand one). The 'upwards' plane has correct normals but the other has inverted normals.



When adding a Glass material the glass acts based on the Index of Refraction (IOR). For normal glass in air the IOR is usually around 1.45 - ie, the default setting for the glass. However, with the flipped normals the mesh actually behaves as if it is a cavity of air within a glass solid and this causes the "surface" to refract unexpectedly and behave as if the IOR is the inverse (in the case of an IOR of 1.45 it behaves as if the IOR is 1/1.45 - ie, 0.69).

The solution to this problem is to either Flip Normals or Recalculate Normals so that the normals are pointing 'out' of the mesh.